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Sauron [17]
3 years ago
10

Dada a função f(x) = ax + b e sabendo-se que f(3) = 5 e f(-2) = -5 calcule f(½)

Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
3 0

Answer:

f(1/2)=0

Step-by-step explanation:

Given this function:

f(x)=ax+b

We need to find the value of:

f(1/2)

This is really simple because the problem give us the following data:

f(3)=5\\\\and\\\\f(-2)=-5

Using this data we can write a 2x2 system of equations like this:

Let:

f(3)=5=a(3)+b\\\\\rightarrow3a+b=5\hspace{10}(1)

and

f(-2)=5=a(-2)+b\\\\\rightarrow-2a+b=-5\hspace{10}(2)

Our system will be:

3a+b=5\hspace{28}(1)\\-2a+b=-5\hspace{10}(2)

We can solve this system using different methods, however I will use elimination method because I believe it is really simple. So:

(1)-(2)\\\\5-(-5)=3a-(-2a)+b-b\\\\10=5a\\\\Solving\hspace{3}for\hspace{3}a\\\\a=\frac{10}{5} =2

Replacing a into (1)

3(2)+b=5\\\\6+b=5\\\\Solving\hspace{3}for\hspace{3}b\\\\b=5-6=-1

Now we found the values of a and b, our function is given by:

f(x)=2x-1

Let's verify it:

f(3)=2(3)-1=6-1=5

f(-2)=2(-2)-1=-4-1=-5

As you can see the function satisfies the data provided by the problem. So we can conclude that it is correct.

Finally, let's find f(x) for x=1/2 :

f(1/2)=2(\frac{1}{2} )-1=\frac{2}{2} -1=1-1=0

Hence:

f(1/2)=0

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